A reaction-diffusion system arising in game theory: existence of solutions and spatial dominance

Hideo Deguchi

doi:10.3934/dcdsb.2017200

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2017, Volume 22, Issue 10: 3891-3901. Doi: 10.3934/dcdsb.2017200

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A reaction-diffusion system arising in game theory: existence of solutions and spatial dominance

Hideo Deguchi

Department of Mathematics, University of Toyama, 3190 Gofuku, Toyama 930-8555, Japan

Received: April 2014

Revised: July 2017

Published: September 2017

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Abstract

The initial value problem for a reaction-diffusion system with discontinuous nonlinearities proposed by Hofbauer in 1999 as an equilibrium selection model in game theory is studied from the viewpoint of the existence and stability of solutions. An equilibrium selection result using the stability of a constant stationary solution is obtained for finite symmetric 2 person games with a 1/2-dominant equilibrium.

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Mathematics Subject Classification: 35Q91, 35A01, 35B35, 35K45, 35R70.

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Figure 1. Condition (B2)

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Figure 2. ⓘ is the set of ${\bf u} \in \Delta$ to which the pure strategy $i$ (i.e., ${\bf e}_i$) is the best reply in the game $(13)$ for $i = 1, 2, 3$. The three dots denote the middle points of the edges.

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Figure 3. ⓘ is the set of ${\bf u} \in \Delta$ to which the pure strategy $i$ (i.e., ${\bf e}_i$) is the best reply in the game $(14)$ for $i = 1, 2, 3$. The three dots denote the middle points of the edges.

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References

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